Math and music are similar in so many aspects. Are the people good at one also good at other? I mean, do mathematicians understand musical theory better than those that have no background in mah?
I've read that Einstein often improvised on violin. Here's a search result[0].
> Einstein's violin playing took a gypsy turn when he improvised, often while thinking about mathematics. He was a very good musician. He could navigate the piano well enough. But his real love was for the violin. Even so, Einstein's violin playing was not of the first rank. Yet such was his love for the violin that he played and practiced anyway. Such is the spell that musical instruments cast on people's minds.
> In addition to studying the classic violin pieces of Bach and Mozart that he adored, Einstein was also given to improvisations. Some have told of the haunting, gypsy-like quality of these rhapsodies. Einstein himself stated that many of his greatest mathematical ideas came when he was improvising on the violin.
Improvisation has little to do with music theory; most Folk and Jazz music is improvised; even what we know today as "classical music" was often improvised in the past; many great composers were also great improvisers.
Good luck improvising without any theory knowledge, especially against a backing band.
Pro folk musicians are some of the most theory adept people I know, my uncle is one and he knows 1000s of songs, and can basically play any song in any key through his theory chops.
Jazz musicians... I mean, cmon, Jazz is all about doing wild things with theory that surprise and amaze you. Good luck being a jazz musician without understanding seventh chords, modal/metric modulation, etc.
No problem if the band operates on known pieces, even possible when the band is from another culture and the specific pieces are not known to the improviser.
Yes, but how does the improviser know which notes are concordant and which dissonant against the chords of the known song without theory? How do they know how to create tension and resolution within the harmonic/melodic progression?
Improvisation doesn't mean "making up random stuff", it means knowing your instrument and the ways in which chords, melodies, harmonies interact, knowing changes and progressions, inside out so well that you naturally can use that knowledge to come up with something unique.
If what you mean is "some musicians can implicitly understand this stuff without knowing the academic language", well yeah, music theory isn't prescriptive, it's a language used to communicate with other musicians. You can get away without knowing the terms, but knowing what it's describing is important.
Edit: I should add, knowing what it's describing is important up until the point that you want to readily communicate with other musicians and have them communicate with you with full understanding, as quickly as possible, sometimes during performance - then the language of music theory becomes very useful.
> how does the improviser know which notes are concordant and which dissonant against the chords of the known song without theory?
A skilled/talented musician just hears that. It's like cooking: a good cook knows from experience which spices go with which dishes, without having to know the basic physics.
> making up random stuff
It always has random components, that's how humans operate; but good improvisers can produce music in real-time which sounds like composed/arranged music; the purpose of music is to entertain and please people; this goal can be fully achieved without any theory or prior arrangement.
Last night I was improvising a melody based on a chord progression I had just come up with. I heard the chord progression in my head without thinking about what the chords were. But then when I thought about it, I knew what they were, tested on my instrument, and wrote them down.
Beginning to melodically improvise on the progression (with no backing) I was initially looking at my chart the whole time and thinking in theoretical terms. But, before long, I was having moments of losing track of where I was in the chart, but my mind's ear and my fingers still knew what to do to keep going within the harmony.
I.e., you reach a point where you have internalised the sound of the chord changes, and you can just hear the lines you want to play, and your fingers just know how to play the notes that you hear.
But to get to the point of being able to do that in a reasonably sophisticated way, one is mightily helped by thinking about things and practising things in a theory-informed way.
An experienced musician with improvisation skills doesn't have to write down chords to be able to improvise. If you have a look at the non-academic music culture as you can still find it e.g. on the country side or in other popular music pieces are passed on by playing them and having the other musicians play along with them and repeat them. Music theory can be helpful, but it's not a "conditio sine qua non".
Oh, absolutely. In fact, I can recall improvising over a song purely by ear, and then coming up with some worse lines once I'd worked what the chords were and written them out.
But music theory isn't on the level of physics, it's not what music is made of, it's more like a recipe - yes, you can intuitively cook a dish from experience, but at some point if you want to communicate that with others you have to write down the names and quantities of the things you're using, the temperatures and timings, and so on. And knowing lots of recipes allows you to much better understand how to tweak and improvise on your existing knowledge by adding new elements or substituting ingredients.
There is a famous quote from Goethe, that aptly describes the situation: "Wenn ihr's nicht fühlt, ihr werdet's nicht erjagen"
> And knowing lots of recipes allows you to much better understand how to tweak and improvise on your existing knowledge
Sure, practice is helpful. And it is to be hoped that the conservatories are also helpful for something, if society invests so much money in them and so many professional musicians come out of them.
Music theory is always "after the fact"; it's a way to teach people what their idols did, even if the idols didn't know or didn't apply the theory. To improvise you first of all require musical talent on both harmonic and rhythmic dimensions, and you need practice. Theory might help, but it is not a prerequisite.
This is not even true across history. "The idols" in jazz did knew and did applied theory.
> To improvise you first of all require musical talent on both harmonic and rhythmic dimensions
I mean, you need ability to keep rhythm and play notes. But beyond that, you absolutely can get away with theory only with basically zero special talent. You wont become world famous, but you will be able to match what the rest of group is playing.
> even what we know today as "classical music" was often improvised in the past; many great composers were also great improvisers.
Also going back to original comment, you seem to put theory and improvisation into some kind of dichotomy. But, both being great composer and great improviser are heavily facilitated by understanding theory.
> "The idols" in jazz did knew and did applied theory
When jazz music appeared, there were no conservatories or theory for it. The first jazz conservatories emerged fifty years later. Today they find many graduates, for example, from Berklee. But this is a development that has only begun in the last forty years. It didn't make the music better, it just made it different.
> You wont become world famous
Very very few world famous exponents of popular music have a formal musical education.
> Very very few world famous exponents of popular music have a formal musical education.
This is just false. If you start to dig into this a little bit, you will easily find connections between almost all famous musicians, and universities. If they didn't have formal education themselves, they often had private lessons from someone with a degree. Or someone in the band had a degree etc. Or in the case of the beatles, the "producer" just happened to be a trained composer who was giving a lot of "suggestions".
Other examples: punk band green day songwriter billie joe had 15 years of lessons with a jazz guitarist with a university degree. Bluegrass guitarist tony rice had private theory lessons with a berklee graduate. etc etc.
It's part of the marketing to downplay the theory and knowledge involved, people want to relate to musicians, and not feel like their being outsmarted, or manipulated by "some formula".
Are you from the industry? I am, with forty years of experience under my belt. Believe me, there is no correlation between success and formal musical education.
I think their point is more that in many cases, you can trace the chain of direct influence to someone with formal training, even if the musicians themselves don't have it.
Obviously, there are also plenty of artists who only have this influence indirectly, through other artists that inspire them. Or in the case of hip hop and electronic, through sampling. So I think their point was overstated.
> When jazz music appeared, there were no conservatories or theory for it. The first jazz conservatories emerged fifty years later.
Yes, to study the tropes and patterns of theory applied by the great jazz musicians, who certainly knew what they were doing with theory, even if "the theory of jazz" didn't exist. You don't have to know "jazz theory" in order to use theory to create a new genre of music that became known as "jazz". There were a community of performing musicians who had at least some formal theory knowledge (if not to a rigorous Berklee standard), who shared ideas and patterns and tropes, which eventually became a recognised genre, and later on an academic field of study.
It's funny, because out of all the niche subgenres of music out there today, jazz is almost certainly one of the most "theory influenced" genres of the last century.
Yeah it's not true at all, just look at russell's lydian chromatic concept for example, and how much new ideas for jazz and improvisation that it spawned. Theory does not only come after practice. Oh how I wish people would stop venting their fantasies of the god gift whenever the subject of music comes up
That's why jazz theory is valuable, sometimes people don't want to spend decades re-learning things that other people have already learned.
Also, I'm just plain not as good a musician as, say, Duke Ellington was, and there's a benefit to being able to understand what he was doing so I can try to imitate that style and incorporate his techniques into my own playing -- I don't want to rediscover all of his lessons completely on my own because I'm not talented enough to do that; very few people are.
Yes, to describe and group together the specific music theory elements that jazz musicians tended to use: sevenths, avoiding triads, modulation, etc. Not because there was no theory intentionally used in jazz music. If you think those guys didn't know what they were doing...
My very amateur musician take: it can have little, or it can have a lot.
One way to 'improvise' is to have an understanding of the relationships between keys and while moving around at pleasing intervals and making interesting chords, regularly jump keys at points where they overlap -- that's .. pretty music-theory driven, and can be very mathematical! There's a lot of fun math in jazz.
It's not the only way to improvise, certainly. But someone who knows the rules can make them run a long way.
Improvisation is like talking. Not all people can do it equally well, and you learn to speak as a child without theory, and without knowing or being aware of the physiological or physical processes, or the syntactic or semantic features of language. You can listen to discussion groups and be well entertained without the speakers following any script or theory.
Can you give an example of a master speaker who doesn't know how to read or write, and are completely ignorant of grammar and how language works? And can you really say that one such example would make speaking mostly unrelated to language theory?
Of course your first exposure is not formal education, but the things I picked up by ear, the speakers had learned in formal education. Nobody becomes an expert in a field, completely detached from the existing body of knowledge. You could learn it only by immersion if you, for some reason, really want to avoid formal education, but you're still using an existing body of knowledge, even though mentally you might not call things "adverbs". And the likely, going that route will be much longer and harder, and also put a limit on how far you can go.
Right, and when you asked your parents/teachers/those around you about aspect of the language you were speaking, did they tell you to not worry about it and just feel it? Or did they explain, well this part of grammar is called an X, and we use it to modify Y, which in turn is a part of Z - such that you could better understand it, communicate it to others better, and generalise the specific thing you'd intuitively learned to a wider aspect of language?
Jazz theory is a way of condensing down and describing to each other what a collective group of musical geniuses did across multiple years.
I don't think theory is strictly necessary, there are great musicians who don't know anything about theory. Theory should never be used as a way of gatekeeping or deriding people's efforts to build things. However, unless you are also a musical genius who has spent decades honing your craft, there will probably be some benefit from learning from the people who came before you.
It's not necessary essential, but very little theory is essential. You can technically be a great game designer without ever looking at other games, you can technically be a great UX designer without learning UX rules. The rules just make it much, much easier to get to that point -- because the rules allow you to more quickly learn from a large body of extremely talented individuals who shaped the entire genre.
Music theory is both the languages of music and the formal study of those languages. Improv musicians communicate with something, and it often looks like the body of music theory around that tradition because the body comes from the tradition.
Trying to separate theory from its basis is folly. Like the scientific method and the body of scientific knowledge, it's important to remember one follows the other, but I'm still employing centuries of science every day even if I can't name it all.
Jazz musicians who can't cite theory don't use 7ths by accident.
That's a very academic perspective which I cannot share as a musician. Music needs no formal specification to exist. It's like a language, but a language for emotional, not rational communication. Btw. science exists by itself as well and doesn't depend on a "scientific method". Like in music, philosophers tried to understand how science works after the fact, and there is a plethora of philosophic optinions how science works. And we can pretty well do science without caring much of all those opinions. The same applies to music.
> Jazz musicians who can't cite theory don't use 7ths by accident.
I don't understand this argument. It's unavoidable to use 7ths, regardless whether the musician can name the interval or not.
I think we're closer than you realize, and I just did a poor job laying out my position. Unfortunately, I lack the language to get closer to what I mean.
> Are the people good at one also good at other? do mathematicians understand musical theory better than those that have no background in math
Music and music theory are two different things. A person who is an expert in music theory is not necessarily a good musician and vice versa. There are approaches to music theory based on mathematics (see book list below); here at the latest, your assumption is likely to be correct, but hardly in general.
Book list:
Mathematics and Music - Composition, Perception, and Performance
Musimathics Volume 1 and 2
Music and Mathematics - From Pythagoras to Fractals
Mathematical and Computational Modeling of Tonality - Theory and Applications
Sure, but it's an add on. Music theory is developed after the fact by analyzing music created by people who (mostly) didn't know the theory. It's a (more or less useful) means to understand what the original creator did.
For Western classical music, this is often claimed and is probably only a little true these days (e.g. Schenker is truly post facto, though illuminating).
However, the theory really was deeply tied to the practice of composition and performance. One of the first exercises Mozart set his composition students was to write out various cadences. Likewise, Bach started his pupils with voice-leading. Theory was also needed for various forms of performance -- look at any manual on continuo playing (this is where the figures on roman numeral notation come from). Handel wrote a manual on continuo playing in which he touches on how to improvise a fugue!
My family is full of music theorists, including a professor of it. I’ve asked this before, and they’re of the thinking that no, one’s aptitude at music theory is not related to a knowledge of mathematics. The professor in my family has in particular seen no relationship between the two in their decades of teaching.
But - importantly - a background of math can be a tremendous asset later in one’s career as a music theorist. It can help provide a unique way of looking at and improving on theory.
I have a degree in mathematics and have studied music for some years. My personal opinion is that they're quite different things. Yes, the underlying theory of music requires some mathematics, but that's it. Once you get into it there's much more "feeling" and "intuition" and "subjectiveness" than math could ever accept.
I don't really think so. The stuff that's covered in the first half of this article is certainly very math-y, but you can be a great musician and not know this stuff. I really think all you need to know is basic arithmetic and the absolute basics of modular arithmetic (akin to learning how 12 o'clock + 1 hour = 1 o'clock, not 13 o'clock).
Becoming a great musician is more about developing your ear, technique, repertoire, etc. It's more similar to learning a foreign language than learning math, in my opinion.
